In Problems 37 and 38 find a quadratic function fx ax2 bx

In Problems 37 and 38, find a quadratic function f(x) = ax^2 + bx + c that satisfies the given conditions. f has the values f(0) = 5, f(l) = 10, f(-1) = 4

Solution

f(x) = ax^2 +bx +c

Points given : f(0) = 5 ; f(1) = 10 ; f(-1) = 4

So, plug these points to find value of a, b , c:

5 = a*0 + b*0 +c ---> c= 5

10 = a+ b + 5 ----> a+b = 5 ---(1)

4 = a -b +5 ----> a-b = -1    ---(2)

Add the two equations to solve for a:

2a = 4 ----> a = 2

b = 3

So, f(x) = 2x^2 + 3x + 5